Just consider me a media dinosaur — that’s certainly what my children think.

You see, I still get a daily paper, in fact two. But I fear that at least one of them, in this case the Washington PostCo.‘s (NYSE:WPO) namesake paper, will go the way of the T-rex. That’s particularly so if the company keeps looking away from the newspaper business to grow revenues and become more diversified.

“Our acquisition of Celtic Healthcare is part of the Post Company’s ongoing strategy of investing in companies with demonstrated earnings potential and strong management teams attracted to our long-term investment horizon. It also fits with our decentralized operating philosophy. We are a diverse group of businesses sharing common goals and values but each with its own identity and workplace culture, and with management responsible for its operations.”

Huh? Really? What part of health care fits in with a flagging sports section? I know times are tough, and I sense perhaps just a tad bit of panic enveloping the Post’s hallowed hallways on 16th Street, but health care? What gives?

The newspaper business is a dying breed. All across the spectrum, hard print advertising is struggling as the world moves to online media and ad models, and the Post is feeling the heat.

Take one media company just beyond the Beltway: AOL (NYSE:AOL). In many ways, AOL is what the Post might want to be, with its Huffington Post model drawing reporters and columnists away from magazines and newspapers and its Patch operation, while still struggling, finding a niche in local news stories in and around the D.C. area that were once strictly the purview of the Post and its Gazette Newspapers operations.

Is AOL a screaming media success story? No, but its current model isn’t a bad template (less the dial-up business, of course).

But the Post is hurting big-time: The publishing division has suffered as print advertising was down 15% in the second quarter to just over $56 million. And as the Washington City Paperreported, although profit was up in the quarter, publishing revenue declined, as did daily and Sunday circulation for The Washington Post.

What’s really starting to hurt is that the Post’s education division, Kaplan (along with other for-profit colleges and schools) is under government scrutiny for misusing funds to attract students, possibly with misleading ads. That’s cutting into a critical component of the Post’s operations.

The Post counts on Kaplan for nearly 58% of its revenue. Earlier this year, its 2011 10-K report report provided a window into some troubling results at the educational services group. The report showed a huge decline in Kaplan’s 2011 results with revenues declining by $500 million, operating income falling from $347 million in 2010 to $89 million and total enrollment sliding from 97,000 to 75,000.

Unfortunately, things aren’t much better on the online side, where most media insiders believe newspapers must somehow find a way to become profitable. According to that same 10-K report, the Post’s online publishing activities, primarily at washingtonpost.com and The Slate Group, reported an 8% revenue decline in 2011 following a 14% increase in 2010. The company is working on cost-cutting, evidenced by the loss of reporters and editors throughout the paper, mostly through early retirement or buyout packages.

Any good news? The Post’s cable-TV division is growing, although only in the areas of high-speed Internet and phone services. Its cable-TV subscriber base is down, and its costs are climbing. Competition for the business is fierce on every front, with satellite providers Dish (NASDAQ:DISH) and DirecTV (NASDAQ:DTV) and cable providers Comcast (NASDAQ:CMCSA) and Verizon (NYSE:VZ) gaining subscribers at the Post’s expense. Besides, the cable group makes up only about 20% of the company revenue.

What makes the Post different however, is its ownership: The company is still essentially owned by the Graham family. It has two classes of stock, with Class A shares being owned by the Graham family who hold unlimited voting rights and the right to elect 70% of the company’s board of directors. And, of course, the company’s biggest non-family shareholder remains Warren Buffett through his Berkshire Hathaway (NYSE:BRK.A, BRK.B), which at the end of the second quarter held over 1.7 million shares according to Nasdaq.com.

Buffett recently retired from the Post’s board of directors after 37 years, but surely his magic touch must still be somewhere in the building.

What’s galling is that while the Grahams fiddle, the company is burning through gobs of cash, dispensing dividends and buying back shares. Indeed, the second quarter’s free cash flow run of $66 million wasn’t nearly enough to cover $93 million in payouts among dividends ($18 million) and buybacks ($75 million). Others can debate whether those share buybacks are well timed, and any dividend increases clearly benefit just a few.

Now, back to health care. Celtic is a $43 million in revenue operation, serving around 2,000 patients from nine locations mostly in Pennsylvania and Maryland. On what level or scale can this acquisition help the Post? Let me answer that question: none.

So, what to make of my favorite paper that I’ve faithfully found on my doorstep for the last 33 years?

The meteor may be a long way off, but it’s headed this way.

Marc Bastow is an Assistant Editor at InvestorPlace.com. As of this writing he was long VZ.